Pull Ups.php
A pull up is a great combination of upper body training as wel as core stability training. The upper body part is a no-brainer: you need your arms and shoulders to pull yourself up and lower yourself back down in a controlled manner. But if you were to relax from the chest down, there's no way you're going to get in a decent number of reps. So, get your core and lower body involved in keeping your body from swinging.
Pull up technique
Grab the bar with your hands, holding your arms (almost!) straight. Pull yourself up until your chin reaches just above the bar. Drop down and repeat. It's that simple. Unless you know exactly what you're doing, try to keep your body as still as possible (other than the vertical movement caused by flexing and relaxing your arms).
Varations
In order to make a regular pull up more interesting, you can take a wider grip, a narrower grip, pull your chest to the bar (instead of your chin, in other words: pulling yourself up higher), raise your knees (or legs) until they make a square angle with your upper body and then perform your pull up, or you can go plyometric style: pull yourself up explosively, briefly let go of the bar at your highest point and then grab it again before lowering yourself.
And the ultimate pull up is - of course - the muscle up: pull yourself up until your hips are at bar level. This is an explosive move that requires both strength and technique. It will take some time and effort to master this pull up varation, but once you can do ten muscle ups in a row, no set of monkey bars will ever scare you again.
If you don't have a pull up bar
Pull ups require some kind of structure that allows you to both hang from it and pull yourself up. A door frame may allow you to hang from it by your fingertips, but unless you're a pro rock climber, you're probably not going to be able to pull yourself up. A step of an open flight of stairs may allow you to hang from and you may be able to pull yourself up, but the step above it may keep you from getting high enough.
Whatever the case: just make do with what you've got. If all you can do is dead-hang from a door frame, go ahead. If you have to do "semi pull ups" because the structure you're working with doesn't allow you to reach high enough with your head, so be it. Doing *something* beats doing nothing every time.